It's an acronym that stands for Metal Oxide Semiconductor Field Effect Transistor. Why some people break that into two words or feel compelled to add a hyphen I don't know. This kind of transistor is used to amplify or switch signal paths. The idea dates back to 1925 as first suggested by Julius Edgar Lilienfeld. He was a Jewish physicist from Ukraine who came to America, not fleeing Germany as was so often the case, but to defend his patents in the 1920s.
The first relevant patent I found was actually filed in Canada in 1925. It's called "Method and apparatus for controlling electric currents" It's reciprocated in the US in 1926 as patent #1745175 and you can see it here. It's opening paragraph explains it's instant relevance. (It's lack of commas vexes me but I quote it verbatim below)
Before the MOSFET we had to use vacuum tubes. The problem with Lilienfeld, is that he didn't publish those oh-so-important scholarly research papers or articles about his works. So on an industrial level he was basically unknown. He was so unknown that in 1934 it was invented and patented again by Dr. Oskar Heil, a German physicist. In 1938 William Shockley invented it again and Bell Labs publicized the hell out of it and so he won a noble prize. The key difference is that Shockley did know about Lilienfeld. He even re-created operational versions from Lilienfeld's patents. Mysteriously Bell-labs managed to avoid referencing Lilienfeld in their own research papers."The invention relates to a method of and apparatus for controlling the flow of an electric current between two terminals of an electrically conducting solid by establishing a third potential between said terminals; and is particularly adaptable to the amplification of oscillating currents such as prevail, for example, in radio communications."
John R. Pierce claims he thought of it, but he didn't make that claim until a year after Bell labs used it in print. He did work with transistors at Bell labs so it may or may not have been him personally. The Bell Telephone Laboratories Technical Memorandum of May 28, 1948 writes it all out as follows:
There are two main types of MOSFETs: nMOSFET and pMOSFETs. (sometimes written as nMOS and pMOS) These both induce a conducting channel between the two contacts we call the source and the drain. It's the channel between them that makes the difference. Currents are negative flowing out of the drain in a pMOSFET and positive flowing out of the drain in a pMOSFET. The "n" and "p" stand for negative and positive if you hadn't guessed. These can also be distinguished as either a Enhancement type or Depletion type. The Depletion Type requires the gate-source voltage (VGS) to switch the device off. The Enhancement Type is the opposite, it requires the gate-source voltage, (VGS) to switch the device on."The device logically belongs in the varistor family, and has the transconductance or transfer impedance of a device having gain, so that this combination is descriptive."
Anyway back to Julius Edgar Lilienfeld. Even though he didn't benefit much from the MOSFET, he got some validation in the 1930s. When Brattain, Bardeen, and Robert Gibney tried to get patents on their first MOSFET and MOSFET-derived ideas, many of their claims were rejected due to the pre-existing Lilienfeld patents. Not that the fight is ever over. Even in 2004 international rectifier and IXYS were fighting over nuances and broadness in their own MOSFET patents that all inescapably reference Lilienfeld. More here. Lilienfeld's legacy lives on today in an eponymous prize awarded by The American Physical Society. More here.